Why Won't You Change Your Mind? Knowledge of Operational Patterns Hinders Learning and Performance on Equations

Abstract

This study examined whether knowledge of arithmetic contributes to difficulties with equations. In Experiment 1, children (ages 7-11) completed tasks to assess their adherence to 3 operational patterns prevalent in arithmetic: (a) the strategy of performing all given operations on all given numbers, (b) the "operations = answer" problem structure, and (c) the concept that the equal sign means "the total." Next, children received a lesson on equations; then, they solved a set of equations. There was a negative relationship between adherence to the operational patterns and learning. In Experiment 2, undergraduates' knowledge of the operational patterns was activated or not. Students whose knowledge was activated did not perform as well on equations. Results suggest that early-learned patterns constrain future learning and performance.